Numbers large and small

Consider this example, from Funding Science in America by James D. Savage (Cambridge University Press, 2000), p. 165:

Since receiving their first $1 million or more in earmarks, seven institutions increased their rank by eight or more places….

When we talk of increasing a number, we usually mean making it larger, but in some cases making the number smaller is called an increase. Why? Because ranks are ordinal numbers, and the highest ordinal number is first, even though it is numerically the smallest number.

This applies to some qualities and ratios as well, such as duration and pace. The object of a racer is to improve their time at covering a given distance, which means to achieve a smaller number for their duration and pace. So a higher speed means a smaller value for time and pace.

If we take this to the mathematical extreme, zero and infinity can have different meanings, too. A racer with a time of zero would instantaneously arrive at the finish line. Their pace would be zero and their speed effectively infinite. So zero can be the highest number as well as the lowest number.